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Lattices and codes : arithmetic for communication systems

Frédérique Oggier

Summary: In this course, we taught show how lattices and codes, both independently and jointly, are used in the context of communication systems. The course was structured as follows : 

  • Introduction to lattices and geometry of numbers
  • Introduction to linear codes and lattices from codes
  • Introduction to number fields and lattices from number fields
  • Introduction to quaternion algebras and codes from quaternion algebras
  • Practical aspects : channel modeling
Mon. 10 Mar, 2025 → Sat. 15 Mar, 2025

Introduction to real dynamical systems with applications

Jorge Mozo Fernández

Summary: The idea of this course is to give an introduction to the theory of real dynamical systems from scratch, focusing on the main elements of qualitative theory: equilibria, periodic orbits, limit cycles, … An outline of the contents is as follows:

Tue. 11 Mar, 2025 → Sat. 22 Mar, 2025

Around the Langlands program

Born in a letter of Robert Langlands to André Weil in 1967, the Langlands program seeks to establish a far-reaching web of conjectures relating seemingly distant areas of mathematics, primarily number theory, representation theory, and algebraic geometry

This thematic month will focus on some of the most important current directions of this program: the geometric Langlands program, the p-adic Langlands program, the geometrization of the Langlands program, and relative Langlands duality.

Mon. 26 Jan, 2026 → Fri. 27 Feb, 2026